Applications of Aqueous Equilibria I: Buffers and Titration Reading: Moore chapter 17, sections 17.1-17.3 Questions for Review and Thought: 16, 20, 24, 26, 28, 32, 36, 38, 42, 44. Key Concepts and Skills: definition of buffer, buffer capacity, titrant, titration, titration curve, equivalence point, endpoint, indicator, acid rain Review calculations of ph using the Henderson-Hasselbach equation, how to select a buffer system to maintain a desired ph, and how to determine ph at any point during the titration of a strong acid and strong base, a strong acid and a weak base, and a strong base and a weak acid. Lecture Topics: I. Buffers A buffer is a solution that resists changes in ph when limited amounts of acids or bases are added. A buffer consists of a weak acid and the salt of its conjugate base, or a weak base and the salt of its conjugate acid. Natural buffers: lakes resist changes in ph (limestone=caco 3, a source of aqueous CO 3 and HCO 3- ). Two potential buffer systems are operative: [HCO 3- ]/[CO 3 ] and [HCO 3- ]/[H 2 CO 3 ] Blood consists of several buffering systems, the most important of which are the [HCO 3 - ]/[H 2 CO 3 ] system and the [H 2 PO 4 - ]/[HPO 4 ] system. Buffers usually consist of approximately equal quantities of a weak acid and its conjugate base or a weak base and its conjugate acid. Example: A 1L aqueous solution contains 0.5 mol CH 3 CO 2 H and 0.5 mol CH 3 CO 2 Na. Calculate the ph of this solution; calculate the ph after 0.01 mol HCl is added; calculate the ph after 0.01 mol NaOH is added. Your equilibria calculations for the original solution should lead to a ph of 4.74 The added HCl, a strong acid, reacts completely with CH 3 CO to produce CH 3 CO 2 H. (How can you easily verify that this is true?). A new equilibrium calculation leads to the new value of ph, 4.27 The added NaOH, a strong base, reacts completely with CH 3 CO 2 H to produce CH 3 CO. A new equilibrium calculation leads to the new value of ph, 4.76 Thus, the buffer system resists large changes in ph by having one component of the conjugate acid/base pair react with the acid or base introduced. How can the ph of a buffer solution be calculated? HA + H 2 O H 3 O + + A -
1. As in the example above, using K a and known concentrations of HA and A -, calculate [H 3 O + ]: K a = [A - ][H 3 O + ]/[HA]; [H 3 O + ] = K a * [HA]/ [A - ] 2. Use the Henderson-Hasselbach equation: since: [H 3 O + ] = K a * [HA]/ [A - ], taking the negative log of both sides gives: ph = pk a + log ([A - ]/[HA]) Henderson-Hasselbach Equation poh=pk b + log ([BH + ]/[B]) for equilibrium: B + H 2 O BH + + - OH Example: At a ph of 7.4, calculate the ratio of [HCO 3 - ]:[H 2 CO 3 ] in the blood (K a (H 2 CO 3 )=4.2 x 10-7 ) Sice pka= -log(4.2x10-7 )= 6.38; ph = pka + log ([HCO 3 - ]/[H 2 CO 3 ]) [HCO 3 - ]/[H 2 CO 3 ]= 10.47 Calculate the ph of blood containing 0.0125M [HCO 3 - ] and 0.0025M [H 2 CO 3 ] ph = pka + log ([HCO 3 - ]/[H 2 CO 3 ]); ph = 7.07 Note that when [A - ]= [HA], [A - ]/[HA]=1 and ph=pka + log 1; ph=pk a To prepare a buffer system to maintain a given ph, match the desired ph to the pk a values listed in the tables of acids. The ph range of a buffer is limited to one ph unit above or below the pka Buffers are only effective when [A - ]/[HA] is between 10 and 0.1 thus a ratio of 100:1 for [A - ]:[HA] does not constitute a buffer; a 50:1 ratio of [HA]:[A - ] does not constitute a buffer sytem. Example: You need a buffer solution with a ph of 10.5. Which conjugate acid/base pair woulf you select and what ratio of [A - ]:[HA] should be combined to form the buffer solution? Use table 17.1 The [HCO 3- ]/[CO 3 ] system has pka=10.32; thus 10.5 = 10.32 + log [CO 3 ]/[HCO 3- ] [CO 3 ]/[HCO 3 - ] = 1.51 II. How does a Buffer work? Add acid: A - + H 3 O + HA + H 2 O Add base: HA + HO - A - + H 2 O What is the limit? If you have 0.1 mol HA and 0.1mol A - Add 0.05 mol HCl.15 mol HA /.05 mol A - still a buffer Add 0.09 mol NaOH.01 mol HA / 0.19 mol A - still a buffer Add 0.2 mol HCl no more A -! ph drops rapidly not a buffer Add 0.15 mol NaOH no more HA! ph rises rapidly not a buffer A buffer s capacity cannot exceed the addition of more strong acid than the amount of conjugate base present, or the addition of more strong base than the amount of conjugate acid present.
III. Acid/ Base Titration An acid/base titration is carried out by slowly adding a measurable amount of acid (or base) of known concentration (the titrant) to a solution of base (or acid) of known volume whose concentration is to be determined. The equivalence point is reached when the stoichiometric amount of titrant has been added to exactly neutralize the acid or base being titrated. Mathematically, at the equivalence point, we can find the unknown concentation c U from the volume (V T ) and concentration (c T ) of the titrant and the volume of the unknown (V U ): c U =V T c T /V U ; for monoprotic weak acids and weak bases, the pka (or pkb) can be found by assessing the ph when [A - ] = [HA], which is the ph when 1/2 the volume of titrant required to reach equivalence point has been added. Two methods allow detection of the equivalence point: 1.) using a ph meter and plotting a titration curve (ph vs. volume of titrant added). The equivalence point is the inflection point of the curve (often found more accurately by plotting dph/dv T or d 2 ph/dv T vs. volume of titrant added) 2.) Use an indicator, a weak acid which changes color in the ph range near the equivalence point. The endpoint of a titration occurs when the indicator changes color. The HIn and In - forms of the indicator have different colors. HIn (aq) + H 2 O (l) In - (aq) + H 3 O + Indicator ph range HIn color In - color Phenolphthalein 8.3-10 colorless red Methyl red 4.4-6.0 red yellow Bromothymol Blue 6.0-7.6 yellow blue Need to choose an indicator that will change color in the desired ph range [HIn]/[In - ] 10, the color of the solution is HIn form [HIn]/[In - ] 0.1, the color of solution is In - [HIn]/[In - ] =1 intermediate color signals endpoint. 3 types of Titrations will be considered: 1.) Strong acid and strong base; 2.) strong base and weak acid; 3.) Strong acid and weak base. Using stoichiometry and the equilibrium principles already studied, you should be able to Determine ph prior to addition of titrant; Determine the ph prior to the equivalence point; Determine the ph at the equivalence point; Determine the ph after the equivalence point; Explain the different regions of titration curves Remember: a strong base reacts completely with a weak acid; a strong acid reacts completely with a weak base. After recalculating [HA] and [A - ], treat as an equilibrium problem. For buffer regions (where [HA=~[A - ]) use the H-H equation. III. Acid Rain Acid rain arises from the pollutants NO 2 and SO 2 that arise from the burning of fossil fuels such as coal, oil and gasoline. 2NO 2 (g) + H 2 O (l) HNO 3 (aq) + HNO 2 (aq) 2SO 2 (g) + O 2 (g) 2 SO 3 (g) SO 3 (g) + H 2 O (l) H 2 SO 4 (aq)
Additional Problems: 1. A buffered solution is made by adding 75.0 grams of sodium acetate to 500 ml of a 0.64M solution of acetic acid at 25 C. What is the ph of the final solution? (assume no volume change). 2. Calculate the ph after 0.01 mol of gaseous HCl is added to 250mL of each of the following solutions: a.) 0.05M NH 3 and 0.15M NH 4 Cl b.) 0.50 M NH 3 and 1.50M NH 4 Cl 3. A student has prepared 1L of a buffer solution containing 0.10M HCN and 0.12 M CN -.K a =7.2 x 10-10 (a) what is the ph of this buffer? (b) What is the ph if 0.01 mol of HCl is added to the buffer? (c) What is the ph if 0.02 mol of NaOH is added to the original buffer? 4. A 310 mg sample of a weak, monoprotic acid was dissolved in sufficient water to prepare 100 ml of solution. It was found that 25.15mL of a standard 0.1M sodium hydroxide solution neutralized the acid to the equivalence point. What is the apparent molecular weight of the unknown acid? 5. A solution of a certain weakly acidic substance was prepared by dissolving and diluting 2.344 g to a final volume of 100mL. In a titration, 42.6 ml of 0.2500M NaOH solution was required to reach a successful endpoint.. The shape of the titration curve was used for the assumption that the acid was monoprotic. The ph at the endpoint was 9.4. (a) Calculate the apparent molecular weight of the unknown acid. (b) Calculate the K a for the acidic substance (c) Calculate the ph of the original 100mL solution (prior to titration) (d) Calculate the ph at the midpoint of the titration (after addition of 21.3 ml of the sodium hydroxide solution) (e) Carefully construct a graph of ph vs. ml of base added for the titration. What would be a suitable indicator for the titration? 6. Calculate the ratio of [NH 3 ]/[NH 4 + ] in each of the following buffered solutions containing ammonia and ammonium chloride. a. ph=9.00 b. ph=8.80 c. ph=10.5 7. A sample of 25 ml of 0.100M NH 3 (K b = 1.8 x 10-5 ) is titrated with 0.100M HCl. Calculate the ph of the sample if you added a TOTAL volume of: a. 0.00mL of the 0.10 M HCl to your sample b. 8.0 ml of the 0.1M HCl to your sample c. 12.5 ml of the 0.10 M HCl to your sample d. 25 ml of the 0.10 M HCl to your sample.